12. Compute \(\vec{F} \times \vec{G}\) for the following two vectors:
a. \(\vec{F} = 8\vec{i} - 3\vec{j} + 3\vec{k}\), \(\vec{G} = -8\vec{i} - 3\vec{j} + \vec{k}\)
b. \(\vec{F} = \vec{i} - 3\vec{k}\), \(\vec{G} = 2\vec{j} + 6\vec{k}\)
13. Given the following vectors with respect to the mobile coordinate frame, M, please
express the vector with respect to the fixed coordinate frame, F, given the mobile frame
is rotated about the axis and angle stated. Use the fundamental rotation matrices for this
problem.
a. \([\vec{p}]\)_M = [0, 2, 1]^T, \theta = \frac{\pi}{3} about the \(f^1\) axis
b. \([\vec{q}]\)_M = [1, 0, -1]^T, \theta = \frac{-\pi}{4} about the \(f^2\) axis
